Question

sketch velocity time graph for the motion of a body from the graph explaining each step calculate Total distance covered by the body​?

Answer 1

Answer:

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Answer 2

The velocity time graph for motion of a body is sketched as enclosed.

Explanation: Calculation details, as deduced from the enclosed velocity time graph / curve, on step by step basis, for total distance covered by the body, are as follows:

The velocity time curve depicted above can be divided into three distinct phases : OA, AB, BT 3

Velocity at points O & T3 is zero & corresponding time datapoints are 0 & T3.

Velocity at points A & B is Vm & corresponding time datapoints are T1 & T2.

Displacement during the timecycle O-T1-T2-T3 = Area covered under the velocity-time curve / graph (trapezium O-A-B-T3-T2-T1-O), illustrated as hatched in the given figure.

Area of trapezium O-A-B-T3-T2-T1-O  

= Area of triangle ΔOAT1 + Area of rectangle ABT2T1 + Area of triangle ΔBT3T2 = ½ [{T2-T1+T3}.Vm]    

(by mensuration formula : area = half of vertical distance x sum of parallel sides of a trapezium)

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